冲击环境下多状态系统可靠性评估和韧性分析

doi:10.12305/j.issn.1001-506X.2026.05.14

Abstract

Abstract:

With the rapid development and intelligent transformation of global industry, system structures are becoming increasingly complex and exhibit multi-state characteristics, and their reliable operation capability directly affects production efficiency and product quality. In response, based on state performance distribution and its transition characteristics, the reliability of multi-state systems under shock environments is evaluated, and then a comprehensive resilience evaluation index is proposed. A comprehensive resilience optimization model of multi-state system is constructed considering reliability and cost constraints, and the effectiveness of the model is verified by taking welding robots as an example. The case results show that under multi-shock scenarios, the comprehensive resilience of the system is restored to 1.000 after maintenance, with a reliability of 0.953. Compared with traditional resilience analysis models, the proposed method can more comprehensively reflect the impacts of external shocks, maintenance and replacement on system resilience, providing a technical approach for the reliable operation of industrial systems.

Key words: reliability, performance, resilience, multi-state system

CLC Number:

N 945

Yongfeng JING, Jiayun CHU, Liang GUAN, Jian JIAO, Hongyan DUI. Multi-state system reliability evaluation and resilience analysis in shock environments[J]. Systems Engineering and Electronics, 2026, 48(5): 1581-1589.

Figures/Tables 10

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References 32

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冲击等级及维修	子系统A（机械本体和减速器）状态转移的时间分布函数
Ⅱ	$ {\varPhi }_{\left(1{,}2\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.018t\right)}^{2}}} $，$ {\varPhi}_{\left(2{,}3\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.014t\right)}^{2.3}}} $，$ {\varPhi }_{\left(3{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.013t\right)}^{2.7}}} $，$ {\varPhi }_{\left(4{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.013t\right)}^{2.9}}} $
Ⅲ	$ {\varPhi }_{\left(1{,}3\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.021t\right)}^{2.3}}} $，$ {\varPhi }_{\left(2{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.02t\right)}^{2.5}}} $，$ {\varPhi }_{\left(3{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.023t\right)}^{2.7}}} $，$ {\varPhi }_{\left(4{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-(0.02t)}^{3.5}}} $
Ⅳ	$ {\varPhi }_{\left(1{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.03t\right)}^{2.5}}} $，$ {\varPhi }_{\left(2{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.03t\right)}^{3.0}}} $，$ {\varPhi }_{\left(3{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.03t\right)}^{3.0}}} $，$ {\varPhi }_{\left(3{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-(0.035t)}^{3.2}}} $
维修时	$ {\varPhi }_{\left(3{,}2\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.05t\right)}^{2}}} $，$ {\varPhi }_{\left(4{,}3\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.032t\right)}^{2}}} $，$ {\varPhi }_{\left(4{,}2\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.022t\right)}^{2}}} $，$ {\varPhi }_{\left(5{,}1\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-(0.05t)}^{3}}} $

时间点	事件	综合韧性	可靠性	总成本
20	第1次II级冲击发生	1.000	1.000	120.132
121.364	第2次II冲击发生	0.471	0.904	465.323
172.614	第2次II级冲击结束	0.278	0.761	1482.173
172.614	第1次预防性维修开始	0.278	0.761	1482.173
188.121	第1次预防性维修结束	0.511	0.887	1593.793
225.312	第3次II冲击发生	0.511	0.887	1815. 413
276.812	第3次II冲击结束	0.322	0.771	2038.147
276.812	第2次预防性维修开始	0.322	0.771	2038.147
291.648	第2次预防性维修结束	0.513	0.912	2185.954
365	仿真结束	0.513	0.912	2373.286

时间点	事件	综合韧性	可靠性	总成本
25	第1次IV级冲击发生	1.000	1.000	286.439
53.562	第1次IV级冲击结束	0.661	0.824	674.423
53.562	第1次事后维修开始	0.661	0.824	674.423
73.639	第1次事后维修结束	0.837	0.943	872.832
124.684	第2次II级冲击发生	0.837	0.943	1026.532
171.742	第2次II级冲击结束	0.572	0.825	1208.493
171.742	预防性维修开始	0.572	0.825	1208.493
188.783	预防性维修结束	0.780	0.907	1327.063
228.106	第3次III级冲击发生	0.780	0.907	1725.392
269.482	第3次III级冲击结束	0.458	0.785	2638.156
269.482	第2次事后维修开始	0.458	0.785	2638.156
298.952	第2次事后维修结束	0.739	0.894	2846.832
301.407	更换维修开始	0.000	0.894	3658.738
310.407	更换维修结束	1.000	0.953	4106.843
365	仿真结束	1.000	0.953	4106.843

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Multi-state system reliability evaluation and resilience analysis in shock environments

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